1. Technical Field
The present invention relates to method and apparatus for designing a photomask for use with production of a semiconductor device, and it particularly relates to the method and apparatus for designing a phase-shifting mask which is suitable for projecting a miniaturized pattern for the semiconductor device production.
2. Background Art
A photomask on which an original mask pattern of a VLSI is drawn is irradiated by an incident ray which is partially coherent. The photomask will be simply referred to as a mask hereinafter. Patterns on the mask are projected on to a semiconductor wafer so as to execute photo lithography. For a projection lithography system realizing the photolithography system, there is required a further miniaturized pattern to be copied on to the wafer.
The minimum feature size of the pattern fabricated is expressed by a degree of resolution therefor. The resolution is evaluated by how accurately two adjacent exposed regions on a resist coated semiconductor substrate can be separated without being overlapped, by utilizing, say, a mask pattern whose light transmissive regions and light shielding regions; are periodically changed. In order to improve the minimum resolution, there is known a method where phase difference is given to the incident ray which passes a pair of adjacent light transmissive regions on the mask.
As for the method where the phase difference is given to the incident ray which passes a pair of adjacent light transmissive regions on the mask, such a method is conventionally known and discussed in a paper entitled "Improving Resolution in Photolithography with a Phase-Shifting Mask" written by Mark D. Levenson et al. (IEEE Transaction on Electron Devices, Vol ED-29 No. 12, 1982, page 1828).
FIG. 2 shows a Levenson type phase shifting mask suggested by the above paper. In the same figure, on mask substrate 14 there are formed a plurality of light-shielding (opaque) regions 16 and light transmissive regions serving as the original images for the patterns and there is provided phase shifter 15 which supplies a phase difference between the incident rays passing through the clear region. The phase shifter 15 is made of transparent material against the incident rays. Phase shifter 15 is arranged to be disposed on either side of a pair of the adjacent light transmissive regions. The phase shifter 15 may be simply referred to as a shifter hereinafter.
The shifter needs to satisfy a condition of EQU d=.lambda./{2(n-1)},
where d is film thickness of the shifter, n an index of refraction and .lambda. a wavelength of the incident ray. There is a phase difference between the ray which passed through the shifter and other transmission rays that didn't pass through the shifter, so that light intensity of the ray a pattern boundary under a light shielding region on the semiconductor substrate becomes near zero. As a result thereof, adjacent regions are separated, thus improving the resolution therefor.
In connection with the paper discussing the Levenson type phase shifting mask and an automatic designing apparatus therefor, there is a paper entitled "Automatic Pattern Generation System for Phase Shifting Mask" authored by Noboru Nomura et al. (Symposium on VLSI Technology, JSAPCAT No.AP911210, pp. 95-96, Oiso, Japan, May. 1991). Nomura et al's technique will be referred to as a first conventional art hereinafter. In Nomura et al's paper, a dynamic random access memory (DRAM) is designed by making use of the apparatus for automatically designing the Levenson type phase shifting masks. In the event that the phase of light rays passing through the pattern contained in input layout are automatically determined, firstly an other arbitrary (or the phase-to-be determined) pattern is selected so that its phase is set to 0.degree.. Thereafter, the phase of arbitrary pattern is set opposite to the phase of pattern facing to the phase-to-be-determined pattern which has a side longest, among patterns whose phases are already determined; when there exist a plurality of patterns facing the longest sides to the phase-to-be determined pattern, a system of Nomura et al. gives warning and aborts a processing.
Moreover, as a second conventional art, there is another paper entitled "Investigating Phase-shifting Mask Layout Issues Using a CAD Toolkit" written by Andrew R. Neureuther et al. (IEDM Technical Digest, pp705-708, 1991). This paper discusses about an automatic designing system where a circuit designer determines a shrink factor for input layout, the phases of the light rays passing through the pattern in the layout are automatically assigned against the shrank pattern, and, if there is a portion where the phase assignments conflict, such portion is notified to the designer.
Moreover, as a third conventional art, there is still another paper entitled An Automatic Shifter Pattern Generator for Levenson-type PSMS (1) written by Kazuko Ooi et al. Extended Abstracts of the 53 rd Autumn Meeting 1992: The Japan society of Applied Physics No.2 p478, lecture no.16P-L-11). In this third conventional art, when the spacing between the light transmissive regions contained in input layout is less than a threshold value, opposite phases are assigned to the pair of the light transmissive regions, and when there exists a conflict spot during the phase assignment, such a spot is notified to the designer. 0oi et al discusses such a method and apparatus which has functions of a phase assignment and a verification against a partially phase assigned layout.
Moreover, as a fourth conventional art, there is still another paper entitled "Algorithm for Phase Shift Mask Design with Priority on Shifter Placement" written by Akemi Moniwa et al. (Digest of Papers Microprocess, '93, pp50-51, 1993). In this paper discussing the phase assignment method, firstly pairs of adjacent light transmissive regions (or apertures) having spacings less than a threshold value are made. These pairs are given weightings, respectively and starting from a pair having heavier weighting factors, the mutual phases are determined to be opposite, so that the conflict spots will occur in a pair having lighter weighting factors.
In the above described first, third and fourth conventional arts, phases are assigned in the geometrically fixed layout. Thus, whether or not there exists a conflict spot in the layout is determined already at a stage of making the layout. For example, referring to FIG. 1, it is impossible to arrange shifters without causing a conflict spot. For instance, in the first conventional art, arrangement will be proper until phase 0.degree. is given to light transmissive region (pattern) 11 and then phase 180.degree. is given to light transmissive region (pattern) 12. However, when a phase is assigned to light transmissive region 13, contradiction will be caused. This is because the light transmissive region 13 is facing to transmissive region 12 in the upper portion indicated by x and facing to transmissive region 11 in the lower portion indicated by y in FIG. 1, and; delete "clear" and insert light transmissive the lengths of side facing with the clear region 13 and clear region 11 are same, and because phase of light transmissive region 11 differs from that of light transmissive region 12, so that a proper phase can not be assigned to the light transmissive region 13, thus causing the contradiction. Even if the order of assigning the phases is changed, it is not possible to arrange the shifter without causing the contradiction.
Moreover, in the third conventional art referring to FIG. 1, when phase 0.degree. is assigned to the light transmission region 11 and phase 180.degree. is assigned to both the light transmissive regions 12 and 13 which are neighboring to the light transmissive region 11 having spacing the threshold, the same phase is assigned to both the light transmissive regions 12 and 13 each of which is neighboring to the other within the threshold spacing, thus causing contradiction. In other words, referring to the light transmissive regions 11 and 13, they are adjacent to each other within the threshold (.rarw..fwdarw.) in a lower region indicated with y in FIG. 1.
Similarly, in the fourth conventional art, the light transmissive regions disposed adjacent to each other need to have opposite phases to each other. Thus, it is impossible to arrange shifters without causing a conflict spot in the layout shown in FIG. 1. In these layouts having contradictory spots (conflict spots), the circuit designer will be required to modify the layout until he/she could eliminate such conflict spots. Since the circuit designer will spend much time in modifying such conflict spots manually, such manual operation is very inefficient.
Moreover, in the second conventional art, a whole layout is scaled down by providing the input layout with certain uniform shrink factor. Thus, the number-of conflict spots will increase as the scale-down operation proceeds. In this second conventional art too, the circuit designer is required to modify the layout about presented conflict spots.
As described above, when the phases are assigned after the layout is completed in the course of designing the Levenson-type phase shifting mask, there often exist conflict spots in the layout. Thus, the designer needs to engage himself/herself in modifying the conflict spots, thus deteriorating designing efficiency. This drawback is a major problem in application of the Levenson-type phase shifting mask.